The surface area \( S \) of a right rectangular prism (also known as a rectangular box) can be calculated using the formula:
\[ S = 2(lw + lh + wh) \]
where \( l \), \( w \), and \( h \) are the lengths of the edges of the prism.
Given that each edge length measures 12.75 cm, we have:
- \( l = 12.75 \) cm
- \( w = 12.75 \) cm
- \( h = 12.75 \) cm
Now, we can calculate the required values:
\[ lw = 12.75 \times 12.75 = 162.5625 , \text{cm}^2 \] \[ lh = 12.75 \times 12.75 = 162.5625 , \text{cm}^2 \] \[ wh = 12.75 \times 12.75 = 162.5625 , \text{cm}^2 \]
Now, sum these areas:
\[ lw + lh + wh = 162.5625 + 162.5625 + 162.5625 = 487.6875 , \text{cm}^2 \]
Finally, multiply by 2 to find the surface area:
\[ S = 2 \times 487.6875 = 975.375 , \text{cm}^2 \]
Rounded to two decimal places, the surface area is:
\[ 975.38 , \text{cm}^2 \]
So, the correct response is:
975.38 cm²